4MA1 Mathematics A: Oct/Nov 2024 Paper 2HHigher Tier Paper 2

Show that 157  2 316  3 34[3]

The length of a table is measured as 1.4 metres correct to one decimal place.

(a)Write down the upper bound of the length of the table.

metres[1]

(b)Write down the lower bound of the length of the table.

metres[1]

The diagram shows triangle PQR

Work out the value of x Give your answer correct to one decimal place.

x = [3]

N is a number.

(a)Work out the value of N

N = [2]

In 2019, the population of a village was 650 In 2020, the population of the village was 806

(b)Work out the percentage increase in the population.

%[3]

Cody has a biased 5-sided spinner, numbered 1, 2, 3, 4, 5

The table gives the probabilities that when the spinner is spun it will land on 2 or on 3 or on 5

The probability that the spinner will land on 1 is the same as the probability that the spinner will land on 4

Cody is going to spin the spinner 400 times.

Work out an estimate for the number of times the spinner will land on 4

[4]

The diagram shows a solid triangular prism.

Work out the total surface area of the triangular prism.

cm²[3]

(a)On the grid, draw the straight line with equation

(i)x = 3 (ii) y = 1 (iii) x  y  7

Label each line with its equation.

[3]

(b)Show, by shading on the grid, the region that satisfies all three of the inequalities

Label the region R[1]

Kim puts 4 bananas in a bag. The mean weight of the 4 bananas in the bag is 145 grams.

Andy puts one more banana into the bag. The mean weight of the 5 bananas in the bag is 142 grams.

Work out the weight of the banana that Andy puts into the bag.

grams[3]

Nisha invests 20 000 euros for 3 years in a savings account. She gets 3.5% per year compound interest.

Work out how much money Nisha will have in her savings account at the end of the 3 years. Give your answer correct to the nearest euro.

euros[3]

All the students in year 10 and all the students in year 11 named their favourite science subject from Biology, Chemistry and Physics.

The pie chart shows information about the results for the year 10 students. The table shows information about the results for the year 11 students.

There are 300 students in year 10 There are 320 students in year 11

More students in year 10 than in year 11 said Biology was their favourite science subject.

How many more?

[5]

ABCDE is a regular pentagon. DEFGHI is a regular hexagon.

AF is a straight line.

Work out the size of angle EAF

[5]

(a)Solve 3x  25  2x  13  x

Show clear algebraic working.

x = [3]

(b)Make c the subject of the formula f 

[4]

The frequency table gives information about the weights, in kilograms, of 60 parcels in a delivery van.

(a)Complete the cumulative frequency table.

[1]

(b)On the grid opposite, draw a cumulative frequency graph for your table.[2]

(c)Use your graph to find an estimate for the median weight of the 60 parcels.

kilograms[1]

(d)Use your graph to find an estimate for the number of these parcels that weigh more than 3.7 kilograms.

[2]

Given that  3³  3^12n

find the value of n Show your working clearly.

n = [3]

Use algebra to show that 0.7 63  4255[2]

A, B, C and D are points on a circle, centre O

(a)(i)Work out the size of angle AOD

[1]

(ii)Give a reason for your answer to part (a)(i)

[1]

(b)Work out the size of angle CAO

[1]

(c)Work out the size of angle ABC

[2]

Here are two vectors.

Calculate the magnitude of the vector

[3]

The straight line L is perpendicular to the straight line with equation 2x  y  9 and passes through the point with coordinates (8, 11)

Find an equation for L Give your answer in the form y  mx  c

[4]

A curve has equation y  ( x

There is only one minimum point on the curve. The coordinates of this minimum point are (5, 4)

Write down the coordinates of the minimum point on the curve with equation

(i)y  ( x  5

( , )[1]

(ii)y  3f x

( , )[1]

(iii)y  ( x  7

( , )[1]

Solve the inequality 10x²  11x  21  0 Show clear algebraic working.

[3]

The Venn diagram shows information about the numbers of items in set A, set B and set C, where x is an integer.

Given that n( A  B)  26

find n( A  C)

[4]

Solve the simultaneous equations

Show clear algebraic working.

[5]

where n is an integer to be found. Show clear algebraic working.[4]

A, B and C are three points on horizontal ground.

AB = 8.4 metres BC = 9.2 metres

B is on a bearing of 067° from A C is on a bearing of 129° from B

Calculate the bearing of A from C Give your answer correct to the nearest degree.

[6]

The diagram shows an equilateral triangle ABC and a circle with centre O

AB, BC and CA are tangents to the circle.

The radius of the circle is x cm

The total area, in cm², of the regions shown shaded in the diagram is nx²

Find the value of n Give your answer correct to 3 significant figures.

n = [5]